Methods of indirect, simulation-based inference for nested and nonnested hypotheses are developed. The methods make use of instrumental models and are applicable in cases where likelihood-based inference is numerically unfeasible. The asymptotic normality of an indirect Wald vector is shown and...

The aim of this paper is to analyze the sensitivity of Value at Risk (VaR) with respect to portfolio allocation. We derive analytical expressions for the first and second derivatives of the Value at Risk, and explain how they can be used to simplify statistical inference and to perform a local...